where are my mistakes? (basic derivatives)

• Oct 23rd 2009, 05:51 AM
golfman44
where are my mistakes? (basic derivatives)
1. y = 6x^5 + 12x^3 + 9x^2 + sqrt(pi^5)

y' = 30x^4 + 36x^2 + 18x ... factor out a 6 -----> y' = 5x^4 + 6x^2 + 3x

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2. y = (x^2 + 1)^3 * (x^3 - 1)^2

use u*dv + v*du -----> (x^2 + 1)^3 * (2)(x^3 - 1)(3x^2) + (x^3 - 1)^2 * (3)(x^2 + 1)^2 (2x)

(6x^2) (x^3 - 1) (x^2 + 1)^3 + (6x) (x^3 - 1)^2 (x^2 + 1)^2

(6x) (x^3 - 1) (x^2 + 1)^2 [(x^3 - 1) + (x^2 + 1) (x)

(6x) (x^3 - 1) (x^2 + 1)^2 (2x^3 + x - 1)

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3. y = (x^3 + 1)/(x^3 - 2)

use low * d.high - high * d.low / low^2

y' = [(x^3 - 2) (3x^2) - ( x^3 + 1) (3x^2)] / (x^3 - 2)^2

(3x^5 - 6x^2 - 3x^5 + 3x^2) / (x^3 - 2)^2

-3x^2 / (x^3 - 2)^2

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4. y = x^2 * sqrt(x + 1)

this one is giving me the most trouble i think...

y' = (x^2) [ 1 / (2x + 2) + 2x(sqrt(x+1))

y' = x^2 / (2x + 2) + 2x(sqrt(x+1)) ... get stuck here.
• Oct 23rd 2009, 06:26 AM
Amer
Quote:

Originally Posted by golfman44
1. y = 6x^5 + 12x^3 + 9x^2 + sqrt(pi^5)

y' = 30x^4 + 36x^2 + 18x ... factor out a 6 -----> y' = 5x^4 + 6x^2 + 3x

------------------------------------------------------------------

2. y = (x^2 + 1)^3 * (x^3 - 1)^2

use u*dv + v*du -----> (x^2 + 1)^3 * (2)(x^3 - 1)(3x^2) + (x^3 - 1)^2 * (3)(x^2 + 1)^2 (2x)

(6x^2) (x^3 - 1) (x^2 + 1)^3 + (6x) (x^3 - 1)^2 (x^2 + 1)^2

(6x) (x^3 - 1) (x^2 + 1)^2 [(x^3 - 1) + (x^2 + 1) (x)

(6x) (x^3 - 1) (x^2 + 1)^2 (2x^3 + x - 1)

------------------------------------------------------------------------

3. y = (x^3 + 1)/(x^3 - 2)

use low * d.high - high * d.low / low^2

y' = [(x^3 - 2) (3x^2) - ( x^3 + 1) (3x^2)] / (x^3 - 2)^2

(3x^5 - 6x^2 - 3x^5 + 3x^2) / (x^3 - 2)^2

-3x^2 / (x^3 - 2)^2

------------------------------------------------------------------
4. y = x^2 * sqrt(x + 1)

this one is giving me the most trouble i think...

y' = (x^2) [ 1 / (2x + 2) + 2x(sqrt(x+1))

y' = x^2 / (2x + 2) + 2x(sqrt(x+1)) ... get stuck here.

$4) y=x^2 \sqrt{x+1}$

$y'= 2x\sqrt{x+1} + x^2\left(\frac{1}{2\sqrt{x+1}}\right)$

you derived other questions correctly